Two numbers are in the ratio $5:3$. If $9$ is subtracted from each,the new ratio becomes $9:5$. What are the two numbers?

What is the fourth proportional to $189, 273$ and $153$?

In two alloys,gold and silver are in the ratios of $4:1$ and $1:3$. After alloying together $10 \text{ kg}$ of the first alloy,$16 \text{ kg}$ of the second,and several kilograms of pure gold,an alloy was obtained in which the ratio of gold to silver was $3:2$. Find the weight of the new alloy (in $\text{kg}$).

The railway fares of air-conditioned sleeper class and ordinary sleeper class are in the ratio $4:1$. The number of passengers who travelled by air-conditioned sleeper and ordinary sleeper classes were in the ratio $3:25$. If the total collection was ₹ $37,000$,how much did air-conditioned sleeper passengers pay (in ₹) (in $,000$)?

₹ $1050$ are divided among $A, B$ and $C$ in such a way that the share of $A$ is $\frac{2}{5}$ of the combined share of $B$ and $C$. $A$ will get (in ₹):

$x$ varies inversely as the square of $y$. Given that $y = 2$ when $x = 1$. The value of $x$ when $y = 6$ will be equal to: